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Let's solve both questions step by step:

### Question 1 (Sequence with Multiplying and Adding):

Given rule: Start at 3, multiply by 2, and then add 4 each time.

1. Start at 3.
2. Multiply by 2: \(3 \times 2 = 6\).
3. Add 4: \(6 + 4 = 10\).
4. Multiply by 2: \(10 \times 2 = 20\).
5. Add 4: \(20 + 4 = 24\).

Thus, the next few terms in the sequence are: **6, 10, 20, 24**.

### Question 2 (Sequence Subtracting Each Time):

Given rule: Subtract 3 each time, and the 10th term is 24.

1. The 10th term is 24.
2. To find the 12th term, we subtract 3 twice:
   - \(24 - 3 = 21\) (11th term).
   - \(21 - 3 = 18\) (12th term).

Thus, the 12th term is **18**.

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Do you need further clarification on any of these steps? Here are some related questions for you to explore:

1. How would you find the 5th term in a similar multiplying and adding sequence?
2. Can you extend the rule of subtracting 3 to calculate earlier terms in the sequence (e.g., the 9th or 8th term)?
3. What happens if you change the rule in the multiplying and adding sequence (e.g., add a different number)?
4. How would you handle a sequence where you multiply by a number and subtract a different number?
5. Can you calculate the 15th term in a sequence that subtracts 2 each time starting from 30?

**Tip:** When working with sequences, always clearly identify the rule so you can consistently apply it to find any term.

Learn how to solve sequences that involve multiplying by 2 and adding 4, as well as sequences where 3 is subtracted each time. This step-by-step guide helps students understand and apply rules for generating terms in sequences. Suitable for students in Grades 4-6.

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